Iceland's Pirate Party, founded in 2012 as a marginal protest group, is now unexpectedly in a position where it could seize power in a country fed up with the political and financial establishment.

Recent public opinion polls have shown the party with 43 percent of voter support, with many Icelanders furious to discover that hundreds of their rich and powerful countrymen were named in the so-called Panama Papers leak which exposed hidden offshore dealings around the world.

Iceland was gearing up Saturday for a major anti-government rally in a test of the opposition's ability to mobilize support following the "Panama Papers" scandal revelations that toppled the premier.

Saturday's demonstration, which is to begin at 1400 GMT, follows five consecutive days of protests sparked by the leak of millions of documents exposing the hidden offshore dealings of political figures and celebrities across the world.

Iceland's prime minister on Tuesday asked the president to dissolve parliament as his government reeled from a political crisis over the so-called Panama Papers, but the president refused.

President Olafur Ragnar Grimsson, who cut short a US visit to return to Reykjavik earlier Tuesday to deal with the crisis, told a televised press conference he wanted to consult the government's junior coalition member before making a decision.

Iceland's prime minister on Monday faced calls to resign after leaked "Panama Papers" tax documents showed he and his wife used an offshore firm to allegedly hide million-dollar investments.

Financial records published by the International Consortium of Investigative Journalists showed that Sigmundur David Gunnlaugsson, 41, and his wife Anna Sigurlaug Palsdottir bought a company in the British Virgin Islands in 2007.

More than 10,000 Icelanders said Monday on Facebook they were ready to welcome Syrian refugees into their homes after the government said it would only let in a handful.

An Icelandic author and professor, Bryndis Bjorgvinsdottir, on Sunday urged fellow citizens to speak out on Facebook if they wanted Iceland, a country of around 330,000 inhabitants, to take in more Syrian refugees.